Question

Find the force $F$ acting on the body of mass $6\text{kg}$ to move it with an acceleration of $1.5{\text{m/s}}^2$. Take $g=10{\text{m/s}}^2$.

• A. $50\text{N}$
• B. $51\text{N}$
• C. $52\text{N}$
• D. $53\text{N}$

Answer 1

The correct option is B $51\text{N}$

The FBDs of the blocks are as shown

From the FBD of $4\text{kg}$ block, we have
$N_1=2g=20\text{N}$
$f_1=\mu N_1=\left(0.42\right)\left(20\right)=8.4\text{N}$

From the FBD of $6\text{kg}$ block, we have
$N_2=N_1+6g=20+60=80\text{N}$
$f_2=\mu N_2=0.42\times 80=33.6\text{N}$

Given, acceleration of the block of mass $6kg$, $a=1.5m/s^2$
$\therefore$ from FBD of $6kg$ block, we get
$F-f_1-f_2=6a$
$\Rightarrow F=6\times 1.5+8.4+33.6=51\text{N}$